THE GAME AND ITS ORIGINS
Jacob and Man in Black are twins. They are on the island with their mother, she goes insane (as Flocke told Kate after Claire tried to kill her in "Recon"), Jacob kills her in the belief that he is saving her and doing the right thing (that's why the first time Flocke and Sawyer see him as a boy in the jungle, he has blood on his hands), Man in Black is angered that his own brother killed their mother, now he hates his brother and sees the murder as proof that human nature is evil and corruptable, he becomes the "Bad Twin".
Then some supernatural shit happens and the Island gives the two twins their special abilities (Jacob's magic touch, ability to "bring" people to the island, Flocke's black smoke form and ability to disguise as dead, unburied people).
Now they start playing their eternal game. That is until Jack says "Screw both of you manipulating jerks" and ends their game somehow.
MiB'S REAL NAME
The Man in Black has doesn't know or remember his name.
He asks Widmore "Do you know who I am?", Widmore says, "You're not John Locke"
He asks Desmond "Do you know who I am?", Desmond says, "You're John Locke".
He is seems angered and dissapointed by Desmond's answer which is why people speculated that he was indeed Locke this whole time, but that theory didn't really pan out.
At some point, when Jacob "steals" his "body" and "humanity", he forgets his original human name.
He keeps asking the question hoping someone can finally give him the answer.